1. Introduction
Drone interceptors, also called interceptor drones or drone interdictions, are unique agile UAVs (unmanned aerial vehicles) that specialize in destroying other drones before they achieve their goals. To accomplish this, an agile UAV launches at a moment’s notice, covers a sizable distance fast, outmaneuvers the opposing drone, and intercepts it. Even though the technology is recent, existing reaction jet systems can provide solutions. Drone interceptors can employ reaction jets to enhance maneuverability and agility [
1,
2]. Drone interceptors with multiple actuators can also increase the fault tolerance ability of the control system [
3,
4].
In the past several decades, various nonlinear and robust control methods have been applied to the control system design of interceptors with multiple actuators [
5]. In [
6], a variable structure control is used in the control system design of interceptors with aerodynamic surfaces and reaction jets. Considering the coupling effect of the flight control system, a second order sliding mode control algorithm is designed for the autopilot system of the interceptor in [
7]. Based on the extended state observer, an autopilot system is proposed to reduce couplings [
8]. For an agile air to air interceptor, a robust backstepping control method is proposed in [
9]. The
θ-
D method is a nonlinear suboptimal algorithm which solves the Hamilton–Jacobi–Bellman equation by adding perturbations to the cost function [
10]. A nonlinear control law of an interceptor with tail fins and reaction jets is developed by the
θ-D method in [
11]. For the longitudinal autopilot design, a suboptimal control algorithm is proposed by the
θ-D method [
12].
μ-synthesis methods are also used in the flight control systems. In [
13], a three-loop control law is developed via
Hꝏ and μ-synthesis methods. Feedback linearization method is an effective approach to design nonlinear flight control systems [
14,
15]. For interceptors with dual control systems, a nonlinear control law is designed by input–output linearization [
16]. However, the above methods do not fully consider the cooperation between discrete and continuous actuators and the problem of fault tolerance.
Since there is actuator redundancy in the interceptor control system, we need to consider the cooperation of different actuators. There are two types of actuators on the interceptor. The aerodynamic control surfaces are continuous while the reaction jets are discrete, which brings difficulty in the design of the control system. Control allocation is one of the effective approaches to solve actuator redundancy and handle actuator faults [
17]. In [
18], an observer-based adaptive variable structure control law is proposed for an interceptor with dual control systems by using a fuzzy allocation algorithm. Considering the autopilot dynamics of the interceptor with aerodynamic control surfaces and reaction jets, an adaptive control law is designed by sliding mode control and optimal control allocation [
2]. For interceptors with blended aero-fin and lateral impulsive thrust, a classical control system with optimal control allocation module is designed in [
19]. Approximate linear models are used in the above methods, which may be limited for implementing in a wide range of flight conditions. To realize the control of UAV with nonlinear characteristics, a fault tolerant controller is proposed by observer-based adaptive dynamic inversion [
4]. Based on the boundary estimation, an adaptive fault-tolerant control algorithm is designed for attitude control under joint actuator faults and uncertain parameters [
20]. An on-line sliding mode control allocation scheme for the fault tolerant control of aircraft is designed in [
21]. Based on quadratic programming and integer linear programming techniques, a fault tolerant control method that includes a fault detection and control allocation algorithms is designed in [
22]. For these optimization-based allocations, the mapping relationship between the virtual control command and the true control inputs is static. Compared to static control allocation, dynamic control allocation provides an additional degree of freedom to account for different actuators [
23].
It is not appropriate to use traditional missiles to intercept drones from the perspective of cost performance, because missiles are more expensive and drones are cheaper. Unlike traditional intercepting missiles [
24,
25,
26], drone interceptors are essentially flying hammers. Ramming interceptors are not single-use munitions, and each unit is actually supposed to fly multiple times. When designing the control system, it becomes more important to consider the fault tolerance of the system.
For the interceptor with aerodynamic surfaces and reaction jets, each pulse thrust has only two states of working and non-working. The thrust cannot be adjusted, and it cannot be stopped after starting until the work is completed, which has obvious discrete and nonlinear working characteristics. At the same time, the aerodynamic control system changes continuously. Therefore, the controller design of the whole is a challenging problem. In order to deal with this hybrid system and actuator fault tolerance problem, a fault weighting dynamic control allocation (FWDCA) algorithm is proposed.
In this paper, a fault tolerant autopilot system for interceptors with aerodynamic surfaces and reaction jets is designed. The autopilot system involves a fault weighting dynamic control allocator and a virtual control law. First, an FWDCA algorithm is developed. Then, a robust virtual control law is designed by using command filtered backstepping [
27] with a parameter update law to produce the virtual control effort signals for the interceptor with uncertainties. The dynamic control allocator distributes the virtual signals to the actuators on the interceptor by the FWDCA strategy.
This paper is organized as follows.
Section 2 presents the nonlinear system model of an interceptor with dual control systems. In
Section 3, the FWDCA algorithm is proposed for the interceptor with aerodynamic surfaces and reaction jets. In
Section 4, a nonlinear virtual control law with a parameter update law is designed. Simulation results are shown in
Section 5 and conclusions are given in
Section 6.
2. Nonlinear Model of the Interceptor
For a drone interceptor with aerodynamic surfaces and reaction jets, the nonlinear model can be expressed as
where
,
,
and
ϕ are the angle of attack, sideslip angle, pitch angle and roll angle, respectively;
,
and
are roll, pitch, and yaw rotational rates, respectively;
,
and
are the moments of inertia;
,
and
are aerodynamic forces along the x, y and z axis, respectively;
,
and
are aerodynamic moments in roll, pitch and yaw, respectively. The aerodynamic forces and moments can be expressed as
where
is dynamic pressure;
is reference surface;
is reference length;
,
,
,
,
and
are aerodynamic coefficients. These coefficients can be expressed by angle-of-attack, sideslip angle, angular rates, and control surface deflection as
where
,
,
and
are aerodynamic force coefficients;
,
,
,
,
,
,
and
are aerodynamic moment coefficients. In order to track the normal acceleration commands, two augmented system states are designed as
where
and
are normal acceleration commands;
and
are normal accelerations. For the divert acceleration is maintained by the aerodynamic lift, the acceleration can be approximately expressed as
where
and
are accelerations along the y and z axes of the interceptor body frame, respectively. Define the system states
,
,
and the control inputs
as
Taking Equations (1)–(3) into account and considering the choices of
,
,
and
, we rearrange the dynamic model of the interceptor as
where the control matrix
and
,
,
,
,
and
can be calculated from Equations (1)–(3) and is not given due to the length of the paper.
,
and
are the system uncertainties. Suppose
,
and
are norm bounded as
where
are unknown constants and
.
5. Simulation Results
In this section, the performance of the proposed fault tolerant control law for the interceptor is investigated by numerical simulations. The tracking acceleration commands are set to be
and
; One pulse thrust can produce a force of 2500 N. The aerodynamic coefficients are obtained from [
16]. The parameters of the virtual control law are chosen as
,
and
; The parameters of command filter are chosen as
and
; The matrices
,
and
are chosen as
,
and
. The parameters
and
are
and
. The desired control inputs
and
are chosen as
and
. In the simulation, the proposed fault tolerant control law is compared with the feedback linearization (FL) control law. The simulation results for the interceptor are shown in
Figure 1,
Figure 2 and
Figure 3.
From
Figure 1,
Figure 2 and
Figure 3, we can see that there is nonminimum phase phenomenon when the interceptor controlled purely by aerodynamic control surfaces. The acceleration response delay is large and the rise time under pure aerodynamic control is about 0.9 s. The introduction of the reaction system effectively compensates for this delay, significantly improving the speed of maneuver tracking. The interceptor with aerodynamic surfaces and reaction jets, under the proposed method and FL approach, there are no minimum phase phenomenon. The norm accelerations under the proposed method and FL are both stabilized after 0.2 s. However, the elevator and rudder deflections under FL are smaller than that under the proposed method and the forces generated by reaction jets under FL are larger than that under the proposed method, because under FL, the reaction jets and tail fins counteract each other after the angle-of-attack and sideslip angle have been generated. Therefore, it is hard to reach the fullest potential of aerodynamic control surfaces by the blending principle of FL. For the agile interceptor with two different types of actuators, the acceleration commands can be tracked by several combinations of inputs of the actuators. In the proposed approach, reaction jets cooperate with aerodynamic control surfaces very well and the fast response of the acceleration command can also be realized with less energy of the reaction jets by regulating the control allocation parameters. When the angle-of-attack and sideslip angle have been generated, the deflections of elevator and rudder under the proposed method are close to the case of aero only. The forces of reaction jets and aerodynamic control surfaces counteract each other under FL, which means the energy of the reaction jets is still consumed when the angle-of-attack and sideslip angle have been generated.
In practical applications, the reaction jets are pulsed control effectors modeled as zero-order holders with a sample time of 25 ms. Simulation results with quantization errors are given in
Figure 4,
Figure 5 and
Figure 6.
The control system tracks the acceleration command smoothly under the proposed method than that under FL when the angle-of-attack and sideslip angle have been generated, because the norm acceleration is maintained by both aerodynamic control surfaces and reaction jets under FL. In
Figure 1,
Figure 2 and
Figure 3, we can see that the forces of the reaction jets under FL in pitch and yaw do not converge to zero when the acceleration commands are tracked. In
Figure 4,
Figure 5 and
Figure 6, when the angle-of-attack and sideslip angle are built up, the reaction jets under FL are still involved in controlling the attitude of the interceptor. The amount of pulse thrust consumption in pitch and yaw under the proposed method are 30 and 18, respectively, while the amount of pulse thrust consumption in pitch and yaw under FL are 57 and 33, respectively. Since the cooperation problem of the two different actuators are fully considered, the response speed of the proposed autopilot system is ensured while the consumption of pulse thrusts is reduced.
In the actuator fault case, we consider the damage of the aerodynamic control surfaces and the reaction control system failure due to the interactions between the airflow and the reaction jets. We suppose that the aerodynamic control surfaces lose 60% effectiveness and the reaction jets lose 50% effectiveness. Simulation results with quantization errors are given in
Figure 7,
Figure 8 and
Figure 9. In
Figure 7,
Figure 8 and
Figure 9, we can see that the autopilot system with FWDCA tracks norm acceleration commands fast and smoothly in the presence of the quantization errors and actuator faults. At 0.1 s, the acceleration under FL becomes negative, which is unexpected. The amount of pulse thrust consumption in pitch and yaw under the proposed method are 41 and 36, respectively, while the amount of pulse thrust consumption in pitch and yaw under FL are 106 and 61, respectively. Compared with no actuator faults, the amount of pulse thrust consumption increases by 60.4% under the proposed method, whereas the amount of pulse thrust consumption increases by 85.6% under the FL. In the case of actuator faults, the cooperation of the actuator of the proposed method is still better than FL.